An Adaptive Inverse Design Method for Photonic Devices Based on Topology Optimization

Abstract

The present invention proposes an adaptive inverse design method for photonic devices based on topology optimization. During the design process, an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics is adopted. On the basis of improving the design efficiency of photonic devices, the present invention ensures that the photonic devices obtained by inverse design have excellent performance indicators. In addition, the designed photonic devices are fully binary, eliminating additional discrete optimization. This not only solves the problem of the degradation of the quality factor of photonic devices caused by discrete optimization, but also simplifies the design process. Further, the photonic devices obtained by inverse design of the present invention have small physical sizes, are easy to scale and integrate, and can be fabricated using conventional semiconductor lithography processes, which is expected to promote the development of photonic integrated chips, especially silicon-based photonic integrated chips.

Description

Technical Field

[0001] The present invention relates to the field of micro-nano photonics, and particularly to an adaptive inverse design method for photonic devices based on topological optimization. Background Art

[0002] With the rapid development of global informatization, people's demand for information is increasing day by day. In this process, the generation, storage, and processing of information highly rely on microelectronic integrated chips, which promotes the continuous improvement of microelectronic integration and the continuous progress of semiconductor process technology. The size of transistors that make up microelectronic chips is getting smaller and smaller, and Moore's Law is facing the risk of failure. The performance improvement space of microelectronic integrated chips is getting smaller and smaller. Against this background, micro-nano photonic integrated chips provide a new solution to solve the dilemmas faced by microelectronic integrated chips.

[0003] Just as microelectronic integrated chips are composed of hundreds of millions of transistors, micro-nano photonic chips are also composed of a large number of discrete photonic devices, and at the same time, the discrete photonic devices are required to have excellent performance and ultra-small size. However, traditional photonic devices are usually designed by forward design methods, which not only have low design efficiency, but also the designed photonic devices have unsatisfactory performance. In addition, the device size is relatively large, which hinders the development of photonic devices towards high performance and small size. This has become a major challenge faced by the development of micro-nano photonic integrated chips.

[0004] In recent years, researchers have gradually turned to inverse design methods for intelligent design of photonic devices, that is, through optimization algorithms to iteratively optimize the quality factor of pre-defined photonic devices until small-size photonic devices that meet the performance requirements are obtained. Compared with traditional forward design methods, the advantages are obvious, which greatly promotes the development of high-performance discrete photonic devices and micro-nano photonic integrated chips.

[0005] Currently, there are mainly two commonly used inverse design methods for photonic devices: one is the direct binary search method, which can obtain photonic devices with excellent performance while maintaining a small size, but the "violent" traversal solution of this method requires a large amount of computing resources and computing time; the other is the topological optimization design method. This design method generally first performs continuous optimization and then discrete optimization, but the additional discrete optimization results in an increase in computational cost and an extension of the design time. More seriously, there are many problems with the designed photonic devices, such as deterioration of the quality factor value (that is, the maximum value of the quality factor when the additional discrete optimization converges is lower than the maximum value of the quality factor when the continuous optimization converges), and the photonic devices are not completely binary after the design is completed. Summary of the Invention

[0006] Aiming at the problems existing in the reverse design of existing photonic devices, the present invention proposes an adaptive reverse design method for photonic devices based on topology optimization. By introducing an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics, it aims to solve the problem that the photonic devices obtained by traditional topology optimization design are not fully binary and the problems of increased computational cost and deteriorated quality factor caused by the need for additional discrete optimization.

[0007] An adaptive reverse design method for photonic devices based on topology optimization, comprising:

[0008] Obtaining a predefined quality factor of a photonic device, wherein the photonic device is composed of two materials with different refractive indices, and the photonic device includes one or more input waveguides and one or more output waveguides;

[0009] Dividing a preset functional area in the photonic device into planar pixel units according to the predefined design accuracy of the photonic device, setting an excitation light source in the input waveguide, and setting a probe in the output waveguide;

[0010] Setting an equivalent relative permittivity regulation factor for all planar pixel units in the preset functional area to form an equivalent relative permittivity regulation factor distribution, and initializing it;

[0011] Fuzzifying and adaptively projecting the initialized equivalent relative permittivity regulation factor distribution, then linearly interpolating the two materials with different refractive indices to obtain an equivalent relative permittivity distribution, substituting the equivalent relative permittivity distribution in the preset functional area into the Maxwell equations and applying an electromagnetic calculation method for solution calculation, obtaining a specific function value of the quality factor based on the solution result of the solution calculation; then iteratively optimizing the preset functional area according to the specific function value of the quality factor until the quality factor converges to the maximum value, obtaining the corresponding equivalent relative permittivity distribution in the preset functional area, and further obtaining a photonic device that meets the design requirements and is fully binary;

[0012] Wherein, during the adaptive projection processing, an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics is used.

[0013] In order to further clarify the adaptive reverse design method for photonic devices based on topology optimization proposed by the present invention, the following makes a detailed description of the basic concepts involved in the present invention:

[0014] The specific quality factor is: after the light source passes through the photonic device, it is the normalization function after the discrete overlap integral of the electromagnetic field distribution detected by the probe in the specified area of the output waveguide and the expected electromagnetic field distribution in the specified area; among them, the calculation method of the discrete overlap integral is: the product of the sum of the elements of the conjugate matrix of the electromagnetic field distribution detected in the specified area of the output waveguide and the sum of the elements of the matrix of the expected electromagnetic field distribution in the specified area;

[0015] The planar pixel unit refers to dividing the preset functional area into a set of regular planar grids according to the predefined design accuracy, and each grid is a planar pixel unit;

[0016] The photonic device is jointly determined by the equivalent relative permittivity distribution corresponding to the input waveguide, the equivalent relative permittivity distribution corresponding to the output waveguide, and the equivalent relative permittivity distribution corresponding to all planar pixel units in the preset functional area;

[0017] The iterative optimization is the process of optimizing the distribution of the equivalent relative permittivity adjustment factors in the preset functional area. Specifically, the following operations are repeated multiple times using an optimization algorithm: regenerating the distribution of the equivalent relative permittivity adjustment factors in the preset functional area, and then transforming the regenerated distribution of the equivalent relative permittivity adjustment factors into a new equivalent relative permittivity distribution after blurring, projection, and linear interpolation processing;

[0018] The complete binarization means that the photonic device obtained after multiple iterations of optimization is only composed of two materials with different refractive indices, the equivalent relative permittivity value of each pixel unit has been determined, and only one of the two values of the first equivalent relative permittivity and the second equivalent relative permittivity can be selected. Among them, the first equivalent relative permittivity represents the equivalent relative permittivity of the low-refractive-index material among the two materials with different refractive indices, and the second equivalent relative permittivity represents the equivalent relative permittivity of the high-refractive-index material among the two materials with different refractive indices.

[0019] To design the three-dimensional photonic device in the embodiments of the present invention, first, the variational refractive index equivalence method or the reciprocal refractive index equivalence method is used to equivalent the desired three-dimensional photonic device into a two-dimensional photonic device. Then, the two-dimensional photonic device is transformed into a number of regular planar pixel units through planar pixel unit division. The equivalent relative permittivity distribution within the preset functional region is substituted into the Maxwell equations for two-dimensional electromagnetic calculation. Based on the solution result of the solution calculation, a specific function value of the quality factor is obtained. Then, an optimization algorithm is used for iterative optimization until the quality factor converges to a maximum value, and the equivalent relative permittivity distribution corresponding to the preset functional region is obtained. Furthermore, a fully binary photonic device that meets the design requirements is obtained. The direct effects brought by the refractive index equivalence method and two-dimensional electromagnetic calculation are small consumption of computing resources and high optimization design efficiency.

[0020] When using the topology optimization method to perform inverse design on photonic devices in the prior art, a very complex quality factor is usually constructed to improve the performance of the photonic device. At the same time, the same quality factor is used for both continuous optimization and additional discrete optimization. During continuous optimization, the equivalent relative permittivity within the preset functional region is allowed to vary continuously, and the quality factor is preferentially converged to the maximum value. During additional discrete optimization, generally, the equivalent permittivity adjustment factor obtained from continuous optimization is used as the initial condition for discrete optimization, and then fuzzification, projection, linear interpolation, electromagnetic calculation, and iterative optimization are continued. This not only increases the overall optimization time but also makes the maximum value of the quality factor obtained when discrete optimization converges lower than the maximum value of the quality factor obtained when continuous optimization converges, that is, the quality factor value of the photonic device deteriorates. Most seriously, even after additional discrete optimization, the photonic device still does not reach the 100% binary state, and there are still some planar pixel units in the "intermediate state", that is, the equivalent relative permittivity values of some planar pixel units are not chosen from the first equivalent relative permittivity and the second equivalent relative permittivity of two pre-selected suitable design materials, but are a value between the first equivalent relative permittivity and the second equivalent relative permittivity. The direct consequence of the photonic device not reaching full binary is that when the designed photonic device is prepared by the process, the equivalent relative permittivity of the planar pixel units of the photonic device in the "intermediate state" must be changed to one of the first equivalent relative permittivity and the second equivalent relative permittivity of the two pre-selected materials. Obviously, this change will increase the complexity of the design, and at the same time, the structure of the photonic device used in the process preparation is not consistent with the structure of the photonic device obtained after the discrete optimization ends. This inconsistency will obviously bring the risk of deterioration of the photonic device performance.

[0021] The present invention breaks through the conventional design thinking. When performing adaptive projection processing, an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics is used. As a result, when the quality factor converges, the obtained photonic device is not only fully binary, ensuring that the structure of the photonic device during process preparation is exactly the same as that at the end of the design of the photonic device, meeting the requirements of process preparation, but also the entire design process is completed adaptively without the need for additional discrete optimization. While solving the problem of deterioration of the quality factor of the photonic device caused by discrete optimization, it also simplifies the design process. In addition, when designing photonic devices with different functions, designers do not need to reconstruct complex quality factors. They only need to fill the expected electromagnetic field distribution into the quality factor and then perform simple initialization and projection parameter configuration to design high-performance photonic devices that are fully binary and meet the requirements of process preparation. Therefore, the method of the present invention has better versatility.

[0022] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention,

[0023] The specific differential processing characteristics are as follows: Two weight factors are introduced into the adaptive projection function, and the two weight factors are used to perform two different projection processes on different plane pixel units in the preset functional area of the photonic device during each iterative optimization process; The specific dynamic adjustment characteristics are as follows: The adaptive projection function always changes dynamically with the number of iterative optimizations.

[0024] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, the expression of the adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics is:

[0025]

[0026] Among them,

[0027]

[0028] β = k·i

[0029] In the formula, is the first equivalent relative permittivity regulation factor of the plane pixel unit after fuzzification processing during each iterative process, is the second equivalent relative permittivity regulation factor of the plane pixel unit after projection processing during each iterative process, and The value ranges are all [0, 1]. β is the projection intensity parameter used in the adaptive projection process during each iteration. k is the linear regulation factor, and k takes any real number greater than 0. i represents the current i-th iteration process, and i takes positive integers. μ is the threshold parameter of the adaptive projection function during each iteration. α1 and α2 are weight factors, and the value ranges of μ, α1, and α2 are all [0, 1]. tanh() represents the hyperbolic tangent function, and · represents the product symbol. Further, in the entire process of the adaptive inverse design of the photonic device, α1, α2, μ, and k in the adaptive projection function are all fixed values and do not change, and α1 > α2.

[0030] The differential processing of the adaptive projection function not only improves the design efficiency but also ensures that the obtained photonic device exhibits excellent performance. Specifically, the adaptive projection function introduces two weight factors, α1 and α2, to achieve the differential projection processing of the first equivalent relative permittivity regulation factor in different plane pixel units within the preset functional area to obtain the second equivalent relative permittivity regulation factor After linear interpolation processing, it is transformed into the equivalent relative permittivity ε. Therefore, α1 and α2 can indirectly differentially process the equivalent relative permittivity ε of each plane pixel unit within the preset functional area of the photonic device. During the iterative optimization process, the weight factor α1 enables the equivalent relative permittivity of the plane pixel units within the preset functional area that are greater than the threshold parameter to change rapidly with the number of iterations, thus reaching the final state earlier, narrowing the solution area of the optimization algorithm, reducing the computational amount, and accelerating the design efficiency; the weight factor α2 enables the equivalent relative permittivity of the plane pixel units within the preset functional area that are less than or equal to the threshold parameter to change slowly with the number of iterations, achieving its fine regulation of the electromagnetic field; in addition, before the quality factor converges, setting different values for the weight factors α1 and α2 can increase the refractive index difference between the equivalent relative permittivities of different plane pixel units, thereby restricting the electromagnetic field to the material with a higher refractive index, reducing energy loss, and enabling the designed photonic device to achieve excellent performance.

[0031] In addition, the above adaptive projection function adopts a two-layer nested structure of the hyperbolic tangent function to increase the projection intensity. At the same time, during the iterative optimization process, β in the adaptive projection function increases dynamically with the number of iterations, making the slope of the projection function gradually increase, and finally achieving the complete binarization of the photonic device, which is beneficial to the realization of the process preparation; moreover, when designing the photonic device, there is no need to perform additional discrete optimization, solving the problem of deterioration of the quality factor value caused by discrete optimization and simplifying the design process.

[0032] According to the adaptive inverse design method of the photonic device based on topology optimization proposed by the present invention, the specific design process includes:

[0033] S1: Obtain the predefined quality factor, preset functional region, input waveguide, output waveguide, and predefined design accuracy of the photonic device, and select two materials with different refractive indices as the design materials;

[0034] S2: According to the predefined design accuracy, divide the preset functional region into M×N regular planar grid cells, where each grid cell is a planar pixel unit;

[0035] S3: Set a light source in the input waveguide to provide an excitation light source for the photonic device; then set a probe in the output waveguide, where the probe is used to detect the electromagnetic field distribution in a specified region of the output waveguide;

[0036] S4: Initialize the equivalent relative permittivity regulation factor in each planar pixel unit within the preset functional region, that is, set an initial equivalent relative permittivity regulation factor for each planar pixel unit within the preset functional region;

[0037] S5: After the initialization process, the equivalent relative permittivity regulation factor of each planar pixel unit is transformed into a first equivalent relative permittivity regulation factor through a fuzzification process, the first equivalent relative permittivity regulation factor is transformed into a second equivalent relative permittivity regulation factor through an adaptive projection process, and the second equivalent relative permittivity regulation factor is transformed into an equivalent relative permittivity after linear interpolation of the two materials with different refractive indices. The equivalent relative permittivities within all planar pixel units then form the equivalent relative permittivity distribution within the preset functional region;

[0038] S6: Substitute the equivalent relative permittivity distribution within the preset functional region into Maxwell's equations and apply an electromagnetic calculation method for solution calculation to obtain the electromagnetic field distribution of the excitation light source passing through the preset functional region. Then, use the probe to measure the electromagnetic field distribution at a specified position of the output waveguide and substitute it into the quality factor for calculation. If the quality factor reaches the maximum value, at this time, the corresponding equivalent relative permittivity distribution within the preset functional region is obtained. Adding the equivalent relative permittivity distribution corresponding to the input waveguide and the equivalent relative permittivity distribution corresponding to the output waveguide gives a photonic device that meets the design requirements; if the quality factor does not reach the maximum value, then perform step S7 operation;

[0039] S7: Iterative optimization, that is, using an optimization algorithm to generate a new equivalent relative permittivity regulation factor for each planar pixel unit in the preset functional area according to the specific function value of the quality factor obtained at the end of the previous iteration, and then repeating steps S5 - S6 until the quality factor converges to the maximum value, obtaining the equivalent relative permittivity distribution corresponding to the preset functional area, and then combining the equivalent relative permittivity distribution of the input waveguide and the equivalent relative permittivity distribution of the output waveguide to obtain a photonic device that meets the design requirements.

[0040] According to the photonic device adaptive inverse design method based on topology optimization proposed by the present invention, the initialization of the equivalent relative permittivity regulation factor includes:

[0041] Set the ρ value of the equivalent relative permittivity regulation factor of all planar pixel units in the preset functional area to the same value, that is, ρ = x0, where x0 ∈ [0, 1];

[0042] Or, randomize the ρ value of the equivalent relative permittivity regulation factor of all planar pixel units in the preset functional area, and the ρ value of the equivalent relative permittivity regulation factor of each planar pixel unit follows a Gaussian-like distribution, so as to achieve initialization; where, the probability density function of the Gaussian-like distribution is as follows:

[0043]

[0044] Or, randomize the ρ value of the equivalent relative permittivity regulation factor of all planar pixel units in the preset functional area, and the ρ value of the equivalent relative permittivity regulation factor of each planar pixel unit follows a U(0, 1) uniform distribution, so as to achieve initialization.

[0045] According to the photonic device adaptive inverse design method based on topology optimization proposed by the present invention, the fuzzy processing of the equivalent relative permittivity regulation factor adopts the following processing method:

[0046]

[0047]

[0048] Among them, is an n×n convolution kernel matrix, and x ij is an element of the convolution kernel matrix; the fuzzy processing can make the photonic device obtained by the design have a larger feature size, that is, planar pixel units with the same equivalent relative permittivity ε appear in clusters, which not only reduces the preparation difficulty of the process, but also improves the manufacturing tolerance of the process device, and is more conducive to the process preparation of the photonic device.

[0049] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, the linear interpolation process for the second equivalent relative permittivity regulation factor is carried out as follows:

[0050]

[0051] Among them, ε represents the equivalent relative permittivity of the planar pixel unit after linear interpolation processing in each iteration process, ε1 is the first equivalent relative permittivity, and ε2 is the second equivalent relative permittivity.

[0052] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, the electromagnetic calculation method is the finite-difference time-domain method and / or the finite-difference frequency-domain method.

[0053] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, the optimization algorithm is the gradient optimization algorithm and / or the quasi-Newton algorithm.

[0054] According to the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, the two materials with different refractive indices are silicon (Si), germanium (Ge), silicon germanide (SiGe), silicon oxide (SiO x ), silicon nitride (SiN x ), silicon carbide (SiC), germanium carbide (GeC), germanium oxide (GeO x ), germanium nitride (GeN x ), air (Air), any two of them. Preferably, the design materials selected in Example 1 are silicon (Si) and silicon dioxide (SiO2), and the design materials selected in Example 2 are silicon (Si) and air (Air).

[0055] The adaptive inverse design method of a photonic device based on topology optimization disclosed by the present invention endows the entire inverse design method with an adaptive characteristic through an adaptive projection function with both differential characteristics and dynamic adjustment characteristics. The adaptive projection function adopts a differential projection processing method, which not only improves the design efficiency, but also ensures that the designed photonic device has excellent performance indicators and meets the design expectations; the hyperbolic tangent function structures nested twice and the dynamic adjustment characteristics in the adaptive projection function realize the complete binaryization of the photonic device, and the designed photonic device can be directly fabricated using conventional semiconductor lithography processes, having good process compatibility, which helps to promote the development of photonic integrated chips, especially silicon-based photonic chips. At the same time, no additional discrete optimization is required during the design process of the photonic device, solving the problem of deterioration of the quality factor caused by discrete optimization and simplifying the design process.

[0056] In addition, the adaptive reverse design method of photonic devices based on topology optimization proposed by the present invention can design various photonic devices according to design requirements. The designed photonic devices include: curved waveguides, crossing waveguides, mode converters, power splitters, polarization splitters, wavelength multiplexers / demultiplexers, mode multiplexers / demultiplexers or grating couplers. It can be widely applied to fields such as optical communication and optical networks. Compared with the traditional forward design method of photonic devices, the photonic devices obtained by the adaptive reverse design method of photonic devices based on topology optimization proposed by the present invention are not restricted by factors such as the physical shape of photonic devices and artificial design experience, and can design device shapes that are difficult to achieve by traditional methods. Moreover, the photonic devices obtained by this method have better performance and smaller sizes than those obtained traditionally, which helps to promote the development of photonic device design, photonic integrated chips, and even silicon-based photonic chips. Description of the Drawings

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0058] Figure 1 Schematic diagram of the process of the adaptive reverse design method of photonic devices based on topology optimization;

[0059] Figure 2 Three-dimensional schematic diagram of the power splitter provided in Embodiment 1 of the present invention;

[0060] Figure 3 Schematic diagram of the design model of the power splitter provided in Embodiment 1 of the present invention;

[0061] Figure 4 Schematic diagram showing that the quality factor of the power splitter provided in Embodiment 1 of the present invention gradually converges as the number of iterations increases;

[0062] Figure 5 Top view contour diagram of the power splitter provided in Embodiment 1 of the present invention and electromagnetic field distribution diagram after inputting an excitation light source;

[0063] Figure 6 Schematic diagram showing the variation of the transmittance of the power splitter provided in Embodiment 1 of the present invention with wavelength.

[0064] Figure 7 Top view contour schematic diagram and partial enlarged view of the power splitter obtained by the traditional reverse design method of photonic devices based on topology optimization and the adaptive reverse design method of photonic devices based on topology optimization proposed in the present invention;

[0065] Figure 8 This is a three-dimensional schematic diagram of the bent waveguide photonic device provided in the second embodiment of the present invention;

[0066] Figure 9 This is a schematic diagram of the design model of the bent waveguide provided in the second embodiment of the present invention;

[0067] Figure 10 This is a schematic diagram showing that the quality factor of the bent waveguide provided in the second embodiment of the present invention gradually converges as the number of iterations increases;

[0068] Figure 11 This is a top view contour diagram of the bent waveguide provided in the second embodiment of the present invention and an electromagnetic field distribution diagram after inputting an excitation light source;

[0069] Figure 12 This is a diagram showing the change of the transmittance of the bent waveguide provided in the second embodiment of the present invention with the wavelength. Detailed implementation manners

[0070] The following combines the drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following two embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0071] Embodiment 1:

[0072] According to Figure 1 The schematic diagram of the adaptive reverse design method flow of the photonic device based on topology optimization provided, in this Embodiment 1, a power splitter based on a silicon-on-insulator (SOI) substrate is designed, and its operating frequency is in the O band of optical communication (the center wavelength is located at 1310 nm). The thickness of the top silicon layer of the SOI substrate is 220 nm, the thickness of the lower silicon dioxide layer is 500 nm, and a 500-nm-thick silicon dioxide capping layer is deposited on the SOI substrate, so that the 220-nm-thick silicon layer is completely surrounded by silicon dioxide. Figure 2 This is a three-dimensional schematic diagram of the power splitter provided in the first embodiment of the present invention, Figure 2 in which (a) is a three-dimensional schematic diagram of the device without adding a silicon dioxide capping layer, Figure 2 in which (b) is a three-dimensional schematic diagram of the device with a silicon dioxide capping layer added. The specific design process is as follows:

[0073] S1: First, define the quality factor:

[0074]

[0075] Among them, is the conjugate matrix of the actual electromagnetic field distribution in the specified area of the output waveguide after the light source passes through the photonic device; E desireThe electromagnetic field distribution matrix expected to be obtained within the specified area of the output waveguide; the subscript D represents the output specified area; ∑ is the summation symbol, the subscript bottom represents the lower output waveguide, and the subscript top represents the upper output waveguide. To normalize the quality factor, a virtual straight waveguide passing through the preset functional area is introduced, and the subscript through is used to represent it;

[0076] Secondly, the design accuracy is set to 40 nm, that is, each planar pixel unit (the smallest unit of design) within the preset functional area is a planar rectangular grid with a side length of 40 nm. Figure 3 Schematic diagram of the design model of the power splitter provided in the first embodiment of the present invention, as Figure 3 shown, the size of the preset functional area 101 is 1.92 μm × 2.4 μm, the widths of the input waveguide 102, the upper output waveguide 103, and the lower output waveguide 104 are 0.4 μm, the spacing between the output waveguides is 1.6 μm, and the width 105 of the perfectly matched layer is 0.8 μm;

[0077] Finally, silicon and silicon dioxide are selected as the design materials, and the three-dimensional photonic device is equivalent to a two-dimensional photonic device using the variational refractive index equivalence method. At this time, the effective refractive index of silicon is n si(neff) = 2.42, and the corresponding equivalent relative permittivity is ε si = 5.86; the effective directivity of silicon dioxide is n sio2(neff) = 1.45, and the corresponding equivalent relative permittivity is ε sio2 = 2.10;

[0078] S2: Divide the preset functional area into 48×60 planar rectangular grids according to the design accuracy. Among them, each grid unit is a planar pixel unit, and 2880 planar pixel units are obtained;

[0079] S3: Set a light source in the input waveguide to provide an excitation light source for the photonic device. Specifically, the input excitation light source is a quasi-TE polarization mode (the main components are H x , H y , E z ); then, set a probe in the output waveguide to detect the electromagnetic field distribution within the specified area of the output waveguide;

[0080] S4: Initialize the equivalent relative permittivity adjustment factor for each planar pixel unit within the preset functional area, that is, set an initial equivalent relative permittivity adjustment factor for each planar pixel unit within the preset functional area. As a preference, in this embodiment, the ρ values of all planar pixel units within the preset functional area are set to a constant, that is, ρ = 0.5;

[0081] S5: After the initialization process, the equivalent relative permittivity regulation factor of each planar pixel unit is transformed into a first equivalent relative permittivity regulation factor through fuzzification processing. The first equivalent relative permittivity regulation factor is transformed into a second equivalent relative permittivity regulation factor through adaptive projection processing. The second equivalent relative permittivity regulation factor is transformed into an equivalent relative permittivity after linear interpolation processing of two different refractive index materials, so as to generate an equivalent relative permittivity distribution within a preset functional area; during the adaptive projection process, it is necessary to set the parameters of the adaptive projection function. Preferably, μ is set to 0.5, α1 is set to 0.5, α2 is set to 0.45, and k is set to 1;

[0082] S6: Substitute the equivalent relative permittivity distribution within the preset functional area into Maxwell's equations and use electromagnetic calculation methods for solution calculation to obtain the electromagnetic field distribution of the excitation light source passing through the preset functional area. Furthermore, use a probe to measure the electromagnetic field distribution at a specified position of the output waveguide and substitute it into the quality factor for calculation. At this time, the quality factor has not reached the maximum value, so the operation of step S7 is performed;

[0083] S7: Iteratively optimize 500 times, that is, use the gradient optimization algorithm to generate a new equivalent relative permittivity regulation factor for each planar pixel unit within the preset functional area according to the specific function value of the quality factor obtained at the end of the previous iteration. Then repeat steps S5 - S6 until the quality factor converges to the maximum value, obtain the equivalent relative permittivity distribution corresponding to the preset functional area, and then combine the equivalent relative permittivity distribution of the input waveguide and the equivalent relative permittivity distribution of the output waveguide to obtain a photonic device that meets the design requirements. Figure 4 FIG. is a schematic diagram showing the quality factor of the power splitter provided in Embodiment 1 of the present invention gradually converging with the increase of the number of iterations. With the increase of the number of iterations, the quality factor gradually converges to the maximum value, and finally a high-performance power splitting device with a small size is obtained.

[0084] Figure 5 FIG. is a top view contour diagram of the power splitter and an electromagnetic field distribution diagram after inputting an excitation light source provided in Embodiment 1 of the present invention. Figure 5 In (a) is the top view contour diagram of the power splitter. Figure 5 In (b) is the electromagnetic field distribution diagram after inputting an excitation light source. From the perspective of the electromagnetic field distribution, the finally obtained photonic device realizes the function of splitting the incident light. Specifically, the transmittance of the lower output waveguide is 48.87%, the transmittance of the upper output waveguide is 49.35%, and the minimum insertion loss of the entire power splitting device is only 0.078 dB. Figure 6It is a schematic diagram showing the variation of the transmittance of the power splitter provided in the first embodiment of the present invention with wavelength. It can be seen that in the wavelength band of 1136 nm - 1546 nm, the transmittances of the two output waveguides both remain above 45%. Therefore, this photonic device has good broadband characteristics.

[0085] In addition, in order to further highlight the advantages of the design method of the present invention, a power splitter obtained by using a traditional inverse design method of a photonic device based on topology optimization is compared with a power splitter obtained by the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention.

[0086] When designing a power splitting device by using a traditional inverse design method of a photonic device based on topology optimization, a projection processing method without adaptive ability is adopted, and continuous optimization is carried out first and then discrete optimization. Continuous optimization is carried out 250 times, where β = 10, and discrete optimization is carried out 250 times, where β = 500. Except for this, the processing of the remaining steps is the same as that of the adaptive inverse design method of a photonic device based on topology optimization proposed by the present invention, so as to achieve the purpose of controlling variables.

[0087] Figure 7 It is a schematic top view and a partial enlarged view of the power splitter obtained by the traditional inverse design method of a photonic device based on topology optimization and the adaptive inverse design method of a photonic device based on topology optimization proposed in the present invention. Figure 7 In (a) shows the schematic top view and the partial enlarged view of the power splitter obtained by using the traditional inverse design method of a photonic device based on topology optimization. It can be seen from the partial enlarged part 201 that the photonic device is not completely binary. As shown by the two planar pixel units 202 and 203 in the figure, the equivalent relative permittivity ε of these planar pixel units does not take either the first equivalent relative permittivity ε1 or the second equivalent relative permittivity ε2, but takes a value between the first equivalent relative permittivity ε1 and the second equivalent relative permittivity ε2. This will cause that when fabricating the photonic device, the equivalent relative permittivity ε of these planar pixel units must be converted into the first equivalent relative permittivity ε1 or the second equivalent relative permittivity ε2 of two different refractive index materials selected in advance. Obviously, this conversion will increase the complexity of the design, and at the same time make the structure of the photonic device used in the fabrication process inconsistent with the structure of the photonic device obtained after the discrete optimization. This inconsistency will further lead to the risk of deterioration of the performance of the photonic device; while Figure 7In Figure (b), there is a schematic top view and a partial enlarged view of a power splitter obtained by using the adaptive inverse design method for photonic devices based on topology optimization proposed in the present invention. It can be seen from the partial enlarged view 204 that each pixel point of the power splitter has been completely binarized, meeting the preparation requirements in the process, and there is no need for subsequent conversion processing as in the traditional inverse design method. Therefore, there is no risk of device performance degradation caused by the inconsistency between the structure of the photonic device used in the process preparation and the structure of the photonic device at the end of the design due to the conversion.

[0088] In addition, the bandwidth of the power splitter with both output transmittances above 45% obtained by the traditional inverse design method for photonic devices based on topology optimization is 361 nm, while the bandwidth of the power splitter with both output transmittances above 45% obtained by the adaptive inverse design method for photonic devices based on topology optimization proposed in the present invention is 410 nm. Therefore, the bandwidth performance of the power splitter obtained by the inverse design method proposed in the present invention is better than that of the power splitter obtained by the traditional inverse method.

[0089] In summary, the power splitter obtained by the adaptive inverse design method for photonic devices based on topology optimization proposed in the present invention not only realizes the complete binarization of the photonic device, which is easy to be realized in the process preparation, but also the bandwidth is increased by 13.57% compared with the power splitter of the same size obtained by the traditional inverse design method for photonic devices based on topology optimization, obtaining a power splitter device with better performance.

[0090] Embodiment 2:

[0091] To further illustrate the generality of the adaptive inverse design method for photonic devices based on topology optimization proposed in the present invention, in this Embodiment 2, a bent waveguide device based on a silicon-on-insulator (SOI) substrate is also designed, and its operating frequency is in the O band of optical communication (the center wavelength is at 1310 nm). The thickness of the top silicon layer of the SOI substrate is 220 nm, and the thickness of the lower silicon dioxide layer is 500 nm. The upper side of the 220-nm-thick top silicon layer is exposed to air. Figure 8 This is a three-dimensional schematic diagram of the bent waveguide photonic device provided in Embodiment 2 of the present invention. The specific design process is as follows:

[0092] S1: First, define the construction quality factor:

[0093]

[0094] Among them, is the conjugate matrix of the actual electromagnetic field distribution in the specified area of the output waveguide after the light source passes through the photonic device; E desireThe electromagnetic field distribution matrix expected to be obtained within the specified area of the output waveguide; ∑ is the summation symbol, D is the specified output area; for normalization, through is a virtual waveguide passing through the preset functional area;

[0095] Secondly, the design accuracy is set to 30 nm, Figure 9 This is a schematic diagram of the design model of the bent waveguide provided in the second embodiment of the present invention. As Figure 9 shown, the size of the preset functional area 301 is 3 μm × 3 μm, the widths of the input waveguide 302 and the output waveguide 303 are 0.48 μm, and the width of the perfectly matched layer 304 is 0.75 μm;

[0096] Finally, silicon and air are selected as the design materials, and the three-dimensional photonic device is equivalent to a two-dimensional photonic device using the variational refractive index equivalence method. At this time, the effective refractive index of silicon is n si(neff) = 2.353, and the corresponding equivalent relative permittivity is ε si = 5.54. The effective directivity of air is n air(neff) = 1, and the corresponding equivalent relative permittivity is ε air = 1;

[0097] S2: Divide the preset functional area into 100×100 planar rectangular grids according to the design accuracy. Among them, each grid unit is a planar pixel unit, and 10,000 different planar pixel units are obtained;

[0098] S3: Set a light source in the input waveguide to provide an excitation light source for the photonic device. Specifically, the input excitation light source is a quasi-TE polarization mode (the main components are H x H y E z ); Then, set a probe in the output waveguide to detect the electromagnetic field distribution within the specified area of the output waveguide;

[0099] S4: Initialize the equivalent relative permittivity adjustment factor in each planar pixel unit within the preset functional area, that is, set an initial equivalent relative permittivity adjustment factor for each planar pixel unit within the preset functional area. As a preference, in the second embodiment, the ρ values of all planar pixel units within the preset functional area are randomly selected, and the ρ value taken by each planar pixel unit follows a quasi-Gaussian distribution;

[0100] S5: After the initialization process, the equivalent relative permittivity regulation factor of each planar pixel unit is transformed into a first equivalent relative permittivity regulation factor through fuzzification processing. The first equivalent relative permittivity regulation factor is transformed into a second equivalent relative permittivity regulation factor through adaptive projection processing. The second equivalent relative permittivity regulation factor is transformed into an equivalent relative permittivity after linear interpolation processing of two different refractive index materials, so as to generate an equivalent relative permittivity distribution within a preset functional area; during the adaptive projection process, it is necessary to set the parameters of the adaptive projection function. Preferably, μ is set to 0.5, α1 is set to 0.5, α2 is set to 0.48, and k is set to 1;

[0101] S6: Substitute the equivalent relative permittivity distribution within the preset functional area into Maxwell's equations and use electromagnetic calculation methods to solve and calculate to obtain the electromagnetic field distribution of the excitation light source passing through the preset functional area. Then, use a probe to measure the electromagnetic field distribution at a specified position of the output waveguide and substitute it into the quality factor for calculation; at this time, the quality factor has not reached the maximum value, so the operation of step S7 is performed;

[0102] S7: Iteratively optimize 500 times, that is, use the gradient optimization algorithm to generate a new equivalent relative permittivity regulation factor for each planar pixel unit within the preset functional area according to the specific function value of the quality factor obtained at the end of the previous iteration. Then repeat steps S5 - S6 until the quality factor converges to the maximum value, obtain the equivalent relative permittivity distribution corresponding to the preset functional area, and then combine the equivalent relative permittivity distribution of the input waveguide and the equivalent relative permittivity distribution of the output waveguide to obtain a photonic device that meets the design requirements. Figure 10 It is a schematic diagram showing that the quality factor of the bent waveguide provided in the second embodiment of the present invention gradually converges as the number of iterations increases. As the number of iterations increases, the quality factor gradually converges to the maximum value, and finally a high-performance bent waveguide device with a small size is obtained.

[0103] Figure 11 It is a top view contour diagram of the bent waveguide and an electromagnetic field distribution diagram after inputting the excitation light source provided in the second embodiment of the present invention. Figure 11 In (a) is the contour diagram of the designed bent waveguide. Figure 11 In (b) is the electromagnetic field distribution after inputting the excitation light source. From the perspective of the electromagnetic field distribution, the finally obtained photonic device realizes the 90° deflection function of the incident light, and the minimum insertion loss of this photonic device is only 0.095 dB. Figure 12 It is a diagram showing the change of the transmittance of the bent waveguide provided in the second embodiment of the present invention with the wavelength. The transmittance remains above 90% in the wavelength range of 1250 nm - 1400 nm.

[0104] As can be seen from the above embodiments, the adaptive inverse design method of photonic devices based on topology optimization proposed by the present invention uses an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics. On the basis of improving the design efficiency of photonic devices, it ensures that the photonic devices designed by inverse design have excellent performance indicators. In addition, the designed photonic devices are completely binary, eliminating the need for additional discrete optimization. This not only solves the problem of the deterioration of the quality factor of photonic devices caused by discrete optimization, but also simplifies the design process. Further, the designed photonic devices can be directly fabricated using conventional semiconductor lithography processes, having good process compatibility, which helps to promote the development of photonic integrated chips, especially silicon-based photonic chips.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive reverse design method for photonic devices based on topology optimization, characterized in that, Including: Obtain a predefined quality factor of a photonic device, where the photonic device is composed of two materials with different refractive indices, and the photonic device includes one or more input waveguides and one or more output waveguides; Divide a preset functional area in the photonic device into planar pixel units according to the predefined design accuracy of the photonic device, set an excitation light source in the input waveguide, and set a probe in the output waveguide; Set an equivalent relative permittivity regulation factor for all planar pixel units in the preset functional area to form an equivalent relative permittivity regulation factor distribution, and perform initialization; Fuzzify and adaptively project the initialized equivalent relative permittivity regulation factor distribution, then perform linear interpolation on the two materials with different refractive indices to obtain an equivalent relative permittivity distribution, substitute the equivalent relative permittivity distribution in the preset functional area into Maxwell's equations and apply an electromagnetic calculation method to solve and calculate, and obtain a specific function value of the quality factor based on the solution result of the solution calculation; then perform iterative optimization on the preset functional area according to the specific function value of the quality factor until the quality factor converges to the maximum value, obtain the corresponding equivalent relative permittivity distribution in the preset functional area, and further obtain a photonic device that meets the design requirements and is fully binary; Wherein, during the adaptive projection processing, an adaptive projection function with both differential processing characteristics and dynamic adjustment characteristics is used; The differential processing characteristics are specifically: two weight factors are introduced in the adaptive projection function, and the two weight factors are used to perform two different projection processes on different planar pixel units in the preset functional area of the photonic device during each iterative optimization process; The dynamic adjustment characteristics are specifically: the adaptive projection function always changes dynamically with the number of iterative optimizations.

2. The adaptive inverse design method of a photonic device based on topological optimization according to claim 1, wherein The expression of the adaptive projection function is: Wherein, β = k·i In the formula, is the first equivalent relative permittivity regulation factor of the planar pixel unit after the fuzzification process in each iteration process, is the second equivalent relative permittivity regulation factor of the planar pixel unit after the projection process in each iteration process, and both have a value range of [0, 1]. β is the projection intensity parameter used in the adaptive projection process in each iteration process. k is a linear regulation factor, and k takes any real number greater than 0. i represents the current i-th iteration process, and i takes positive integers. μ is the threshold parameter of the adaptive projection function in each iteration process. α1 and α2 are weight factors, and the value ranges of μ, α1, and α2 are all [0, 1]. tanh() represents the hyperbolic tangent function, and · represents the product symbol. Further, in the entire process of the adaptive inverse design of the photonic device, α1, α2, μ, and k in the adaptive projection function are all fixed values and do not change, and α1 > α2.

3. The adaptive inverse design method of a photonic device based on topological optimization according to claim 1, characterized in that The quality factor is specifically: after the light source passes through the photonic device, a normalized function after discrete overlapping integration of the electromagnetic field distribution detected by the probe in the specified area of the output waveguide and the expected electromagnetic field distribution in the specified area; wherein, the calculation method of the discrete overlapping integration is: perform a product process on the sum result of each element of the conjugate matrix of the electromagnetic field distribution detected in the specified area of the output waveguide and the sum result of each element of the matrix of the expected electromagnetic field distribution in the specified area; The planar pixel unit refers to dividing the preset functional area into a set of regular planar grids according to the predefined design accuracy, and each grid is a planar pixel unit; The photonic device is jointly determined by the equivalent relative permittivity distribution corresponding to the input waveguide, the equivalent relative permittivity distribution corresponding to the output waveguide, and the equivalent relative permittivity distribution corresponding to all planar pixel units in the preset functional area; The iterative optimization is a process of optimizing the distribution of the equivalent relative permittivity regulation factors within the preset functional region; specifically, the following operations are repeated multiple times using an optimization algorithm: regenerating the distribution of the equivalent relative permittivity regulation factors within the preset functional region, and then transforming the regenerated distribution of the equivalent relative permittivity regulation factors into a new equivalent relative permittivity distribution after fuzzification, projection, and linear interpolation processing; The complete binarization means that the photon device obtained after multiple iterative optimizations is composed of only two materials with different refractive indices, the equivalent relative permittivity value of each pixel unit has been determined, and only one of the two values of the first equivalent relative permittivity and the second equivalent relative permittivity can be selected. Among them, the first equivalent relative permittivity represents the equivalent relative permittivity of the low-refractive-index material among the two materials with different refractive indices, and the second equivalent relative permittivity represents the equivalent relative permittivity of the high-refractive-index material among the two materials with different refractive indices.

4. The adaptive inverse design method of a photonic device based on topological optimization according to claim 1, characterized in that, The specific design process of the method includes: S1: Obtain the predefined quality factor, preset functional region, input waveguide, output waveguide, predefined design accuracy of the photon device, and select two materials with different refractive indices as the design materials; S2: According to the predefined design accuracy, divide the preset functional region into M×N regular planar grid cells, where each grid cell is a planar pixel unit; S3: Set a light source in the input waveguide to provide an excitation light source for the photon device; then set a probe in the output waveguide, where the probe is used to detect the electromagnetic field distribution in a specified region of the output waveguide; S4: Initialize the equivalent relative permittivity regulation factors in each planar pixel unit within the preset functional region, that is, set an initial equivalent relative permittivity regulation factor for each planar pixel unit within the preset functional region; S5: The equivalent relative permittivity regulation factor of each planar pixel unit after the initialization process is transformed into a first equivalent relative permittivity regulation factor through fuzzification processing, the first equivalent relative permittivity regulation factor is transformed into a second equivalent relative permittivity regulation factor through adaptive projection processing, and the second equivalent relative permittivity regulation factor is transformed into an equivalent relative permittivity through linear interpolation processing of the two materials with different refractive indices. The equivalent relative permittivities in all planar pixel units then form the equivalent relative permittivity distribution within the preset functional region; S6: Substitute the equivalent relative permittivity distribution within the preset functional region into Maxwell's equations and solve using electromagnetic calculation methods to obtain the electromagnetic field distribution of the excitation light source passing through the preset functional region. Then, use a probe to measure the electromagnetic field distribution at a specified position of the output waveguide and substitute it into the quality factor for calculation. If the quality factor reaches the maximum value, the corresponding equivalent relative permittivity distribution within the preset functional region is obtained at this time. Combining the equivalent relative permittivity distribution corresponding to the input waveguide and the equivalent relative permittivity distribution corresponding to the output waveguide gives a photonic device that meets the design requirements. If the quality factor does not reach the maximum value, perform the operation in step S7; S7: Iterative optimization, that is, use an optimization algorithm to generate a new equivalent relative permittivity adjustment factor for each planar pixel unit within the preset functional region according to the specific function value of the quality factor obtained at the end of the previous iteration. Then repeat steps S5 - S6 until the quality factor converges to the maximum value, obtain the equivalent relative permittivity distribution corresponding to the preset functional region, and then combine the equivalent relative permittivity distribution of the input waveguide and the equivalent relative permittivity distribution of the output waveguide to obtain a photonic device that meets the design requirements.

5. The specific design process of the adaptive inverse design method for photonic devices based on topological optimization according to claim 4, characterized in that Initialize the equivalent relative permittivity adjustment factor, including: Set the ρ value of the equivalent relative permittivity adjustment factor for all planar pixel units within the preset functional region to the same value, that is, ρ = x0, where x0 ∈ [0, 1]; Or, randomly assign values to the ρ values of the equivalent relative permittivity adjustment factors for all planar pixel units within the preset functional region, and the ρ value of the equivalent relative permittivity adjustment factor for each planar pixel unit follows a quasi-Gaussian distribution, thereby achieving initialization. Among them, the probability density function of the quasi-Gaussian distribution is as follows: Or, randomly assign values to the ρ values of the equivalent relative permittivity adjustment factors for all planar pixel units within the preset functional region, and the ρ value of the equivalent relative permittivity adjustment factor for each planar pixel unit follows a U(0, 1) uniform distribution, thereby achieving initialization.

6. The specific design process of the adaptive inverse design method for photonic devices based on topological optimization according to claim 4, characterized in that, The electromagnetic calculation method is the finite-difference time-domain method and / or the finite-difference frequency-domain method.

7. The specific design process of the adaptive inverse design method for a photonic device based on topological optimization according to claim 4, characterized in that The optimization algorithm is the gradient optimization algorithm and / or the quasi-Newton algorithm.

8. The specific design process of the adaptive inverse design method for a photonic device based on topological optimization according to claim 4, characterized in that The two materials with different refractive indices are any two of silicon, germanium, silicon germanide, silicon oxide, silicon nitride, silicon carbide, germanium carbide, germanium oxide, germanium nitride, and air.

9. The adaptive inverse design method of a photonic device based on topological optimization according to any one of claims 1-8, characterized in that The designed photonic device includes: a bent waveguide, a cross waveguide, a mode converter, a power splitter, a polarization splitter, a wavelength multiplexer / demultiplexer, a mode multiplexer / demultiplexer, or a grating coupler.

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